PSI - Issue 13

Takayuki Kitamura et al. / Procedia Structural Integrity 13 (2018) 2180–2183 Author name / StructuralIntegrity Procedia 00 (2018) 000 – 000

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2. Development in experimental methodology

For the experimental investigation of fracture toughness in the atomic (nanometer) scale, special attention must be paid on every procedure and process in the methodology. 2.1. Selection of Material The stress distribution near the crack tip is strongly affected by the defects in the atomic scale existed in the area. Since the stress singularity zone with the size of several nanometers is focused in this ultimate research, the defects even in a few nanometer scale have be carefu lly excluded. In other words, the material must be “extremely clean” in the atomic scale. Then, single crystal of silicon is selected in this investigation as the tested material, which does not includes a grain boundary (2 dimensional (2D) defect in the atomic scale) and a dislocation (1D). Although the vacancies (0D) cannot be excluded due to its entropy, the density is low enough in the stress-singular area. Other merits are that it is available in market and that it possesses is industrial importance in terms of engineering field such as electrical devises and MEMS/NEMS. The fracture toughness requires propagation of straight crack. Considering the scale of testing, the crack should have straight propagation in the atomic scale keeping the crack opening mode (Mode I). In other words, the crack propagation must be “extremely clean” in the atomic scale. It is well known that silicon shows cleavage fracture where the crack propagates along a particular crystallographic plane. Thus, setting the cracking direction on the plane (110) of tested material in the specimen, this requirement is attainable. 2.2. Specimen design Considering the requirements for the specimen such as gripping, loading arraignment, Mode I cracking and fabrication process, the double cantilever type one as illustrated in Fig.1 is selected for the testing in this investigation. A sharp notch is prepared at the top for applying the opening displacement. This does not need the gripping of specimen at one side for the loading while the bottom side is fixed on a substrate. The crystallographic orientation of single crystal silicon is carefully aligned as shown in Fig.1 in order to make the straight cracking along the cleavage fracture plane.

Figure 1 Double cantilever specimen for fracture toughness in nanometer scale

The opening displacement applied by a diamond chip provides the cracking load under the pure Mode I condition. The fracture toughness is defined as the beginning of unstable cracking. The instability in the fracture is sensitive to the crack tip (notch root) radius. The standard in the fracture usually requires the cracking from a slit (crack) with an adequate sharp tip radius. In the toughness testing in nanometer scale, it means the necessity of radius with the atomistic scale for the starter of cracking. In other words, a “extremely clean” pre -crack in atomic scale is inevitable for the accurate evaluation of fracture toughness. Then, we introduce a pre-crack by the preliminary loading using the above method, before the fracture toughness testing. If the pre-crack is too long, the upper part is cut for adjusting the length. The stress distribution ahead of the crack tip at the critical load obtained by the fracture toughness testing is analyzed by the Finite Element Method (FEM) using a commercial software, ABAQUS. The material constants used are listed in Table 1. As the silicon is a brittle material, the stress, σ ij , near the crack tip has the form,   / ij I K r f     where K I is the Mode I stress intensity factor, (r, θ) are the polar coordinate with the origin at the crack tip and f is the function of θ . This singular stress field governs only the crack tip area , and the size of singular zone is denoted as Λ.